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Lesson Plan : Extreme values of functions
Teacher Name: | Melissa Lones |
Grade: | Grade 11-12 |
Subject: | Math |
Topic: | Find the absolute maximum, minimum values of a function. Determine where the function is increasing and decreasing. |
Content: | Definition of absolute extreme values, the exreme value theorem, definition of local extreme values and theorem of local extreme values. 2.03 Interpret the derivative as a function. b. Indentify relationship between the increasing and decreasing behavior of f and the sign of f'. |
Goals: | The student will evaluate when a function is increasing and decreasing by taking the first derivative of the function. This will allow the students to determine the maximum and minimum values of the function. |
Objectives: | Given a function the student will first graph it and determine graphically where the function is increasing and decreasing. The student will then take the first derivative of the function and find the critical points and compare them to their outcomes from the original graph to determine how to utilize the critical points to evaluate the graph. |
Materials: | TI-83+ calculator, Smartboard, worksheet with problems. |
Introduction: | Find the first derivative of 3 posted problems. Students will enter their answers on the smartboard. |
Development: | Have the students graph the first function on their calculator, then I will post the same graph on the smartboard. Then I will have them print it out and graph the first derivative of that same equation. We will discuss the first graph and the increasing and decreasing behavior of the graph. Once we have a consensus, we will look at the graph of the first derivative. We will then compare the two graphs and how they relate. Then I will show them how to do the same problem mathematically. |
Practice: | I will post 5 problems on the smartboard for the students to complete mathematically. The students will group up into 5 groups and each group will complete a problem. They will then go to the board and explain how they came up with the answer. |
Accommodations: | This is an AP class, there are no students with accommodations |
Checking For Understanding: | Monitor the students progress on the worksheet to make sure that they understand the concepts. |
Closure: | Put up two graphs on the smartboard. Have the students graphically determine when the orginal graph is increasing and decreasing. |
Evaluation: | Check worksheet and mini-quiz on the material. This material is a two part lesson and the next step is a mirror image of the first but involves concavity. |
Teacher Reflections: | The students always seem to understand this lesson. Seeing the graphs of the functions helps them solidify the results that the find mathematically. |
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